Vol. 39, No. 3, 1971

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Modules over universal regular rings

Roger Allen Wiegand

Vol. 39 (1971), No. 3, 807–819

To each commutive ring R there is associated a certain commutative regular ring R. The ring R is in fact an R-algebra. It is shown that RR is never flat, unless R is itself regular. The functor taking R to R preserves direct limits, and, in certain cases, tensor products. It is shown that if R is weakly noetherian then the global dimension of R less than or equal to the Krull dimension of R. Necessary and sufficient conditions that R be a quotient ring of R are determined.

Mathematical Subject Classification 2000
Primary: 13C10
Received: 4 December 1970
Revised: 9 July 1971
Published: 1 December 1971
Roger Allen Wiegand